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The simplest sort of analysis can be performed if all the animals survived for the whole length of the expariment - and in practice the same sort of analysis is performed provided a reasonable fraction survived that long and provided there were not too many early deaths. In that case, we can simpVy list the dose groups and the numbers of animals with tumors compared with the total number of animals examined; for example: Dose Number with Tumor Number Examined 0 (control) 10 50 0.5 x MTD 25 50 MTD 30 50 However, things are not usually this simple. Similar results are available for Many different sites a Many different tumor types Combinations of these as will be seen in the examples to follow. To determine whether the rate of cancer has been increased involves comparing the proportion with tumor in the control group with the proportion with tumor in the dosed groups, and deciding whether there is a significant increase in any dosed group(s). The choice of which sites and/or types of tumors to combine before performing such statistical tests can be difficult. Generally, various grades of tumors (nodules, adenomas, carcinomcas) may be combined for any given site. In addition to the simple numbers of animals with tumor, there is additional information available which mai y be used in more complicated cases. The date of death of each animal is recorded, and may be taken into account in time-adjusted analyses of tumor incidence and in the life-table tests meftfioned on the appended material. . IU O N Cst ~11 ~ ~ ~ 11 ~

For risk assessment purposes, it is necessary to make various assumptions about the behavior of animals in experiments like these. For example, it is assumed that: • Animals are affected independently (a tumor in one animal has no effect on any other animal). • Animals are equally likely to be affected • Each animal receives the same dose and so forth. It is assumed that cage effects, littermate effects, the effects of heating, lighting, stress etc. are either not present, or are randomized among all the animals in such a way that there will be no effect on 1he final analysis. With such assumptions, the probability of an animal having a tumor is related to the dose by some sort of dose-response relationship, so that at any given dose this probability can be computed.. The observed results, a number of animals with tumor out of a larger number examined, is then a binomial sample with this probability. In practice, we don't know what the dose-response relationship is - we wish to estimate it from the results. But we assume that we know thO ,3HAPE of the dose-response relationship (specified by a mathematical formula), so that all that is required is to estimate some PARAMETERS in the mathematical formula. For example, the E.P.A. uses a dose-response relationship of the form: p=1-exp{-(qo+q,d+q2d2+...+qk-,dk-1 )I when there are k doses in an experiment, where p is the lifetime probability of tumor at dose d. It is usual -to use a maximum likelihood technique to estimate the various parameters q0, q1, q2, ... qk_,, given 'the observed numbers of animals with tumors and the numbers of animals examined at each dose. In cases where there is appreciable early mortality in the experiment, so that the observed numbers of animals with tumors are likely to be underestimates of what would have been observed at the end of a perfect experiment, one can make modifications to the dose response relationship, just as one can make life-table adjustments to standard statistical tests. One technique used is to modify the dose response curve to explicitly include length of life, using the idea that probability of tumor is likely to increase with a power of age (see page 2): p = 1 -exp{-(qo+q,d+q2d2+...+qk-,dk-') (t/L)"~ where t is t'he age at death, and L is a standard lifetime. The parameter n can either be fixed at some reasonable value (in the range 2 to 11), or estimated from the experimental results. This technique suffers from the same limitations as the usual modifications to the standard statistical 12

tests -- one has to introduce additional assumptions in order to apply it. In this case, one has to decide whether the tumors were a cause of death, or simply incidental. An alternative technique used when there is early mortality is to estimate the age dependence directly from the data, using a (so-called) non-parametric technique. This approach has been used to assemble a large database of comparable analyses of animal bioassays. This msV hodofogy has taken the raw results of the animal experiment, and summarized them in the form of a dose-response curve with known parameters. It is also possible to estimate how uncertain one is about a given parameter, using the same maximum likelihood techniques used to obtain point estimates of them - indeed, one can plot the uncertainty distribution for any of the parameters. For example, for the parameter q, (which will turn out to be the one of interest), we can plot the probability that q, lies below any given value: ..... . . .. .~ . __..... ....::- - 1; i i ... . . ,.... . . ... f. ...... '--. ..:.... .., x R In particular, we can find that value q,* such that there is 95% probability that q, < q,*. However, it is important to note that the uncertainty distribution so plotted contains only the uncertain#y due to the numerical size of the experiment - the uncertainty that arises because we used a small number of animals, instead of an infinite number. It does not include the uncertainties which must be present because of the shakiness of all our assumptions -- i.e. the major urn;Ortainties. I ._ _..._, 13

7 The Two Major Extrapolations The assumptions made so far have allowed us to parametrize an animal dose-response relationship, obtaining values for the parameters which are presumably reasonably appropriate for high doses. Strictly speaking, this parametrization of the dose-response curve only enables us to estimate'the results we would expect to see at high doses in animals -the dose-response relationsh;ip can only be relied on to interpolate between high doses and perhaps to extrapolate a short distance outside the experimental range of doses. The problem now is to perform two extrapolaiaons - from animals to humans, and from high dose to low dose: Animal High Dose Low Dose Human Observed ~ ~ ~ ~ Required LOGICALL Y there are two distinct routes to follow in this extrapolation, since there are logically two distinct dose-response curves involved (see below). One can extrapolate from high dose to low dose using the ANIMAL dose-response curve, and then extrapolate to humans (dashed lines), or extrapolate to humans at high doses and then use a HUMAN dose-response curve to extrapolatE~ to low doses. We have seen how to estimate the parameters of the (high dose region of) the animal dose-respcnse curve. In practice, the same curve (with the same parameters) is used to extrapolate to low doses, by building into the mathematical structure of the dose-tesponse curve all our as3umptions about low dose behavior. How is this relevant for estimating human risk? Consider a generalized situation in which we wish to estimate the response (R) of humans to some dose (D) of material, when there is a response (r) in some experimental system at dose (d). Notice that nothing implies that r, R measure tha same sort of response - they could be completely different (r could be acute toxicity to the lung of a mouse, R could be skin rashes in humans). Similarly, the dose measures d, D may be completely different. In the case immediately at hand, r is the lifetime probability of tumor in animals, iand d is a dose as measured in the animal experiment. There are other cases of practical importance however - r might be some measure of response (such as number of 14

revertants per culture dish) in a mutagenesis bioassay, with d the dose applied to each culture dish. l Sysl,em -> Arbitrary Animal bioassay Human example Re>ponse r p (lifetime probY. of R tumor Dose measure d d (as used in expt.) D Dose-response r = f(d; a,b,c,..,t) p=1-exp{-(qo+q,d+..)} R = F(D; A,B,C,..,t) curve What is required is some connection between the parameters a,b,c,... of the dose-response relationship in the experimental system and the parameters A,B,C,... of the human dose-response relationship. These parameters presumably include those mentioned in Section 6, and I have explicitly included age amongst them. Given such a connection, the extrapolation to humans of the results in the animal studies is perfectly straightforward. The problem lies in finding the connection. Once such a conn-', ;;ion is found (by whatever means) we have the methodology for the two extrapolations required. Notice the difference between what is done in the two distinct pathways of extrapolation mentioned above: In the first, the shape of the dose-response curves are examined, and it is decided how they may be (separately) extrapolated to low doses. Then some relationship is postulated between the parameters of the dose-response curves at low doses (it has to be postulated, since nothing can be measured at such low doses). One potential advantage of this approach is that the animal dose-respanse curve could be measured, in principle and by heroic experimentation, down to lower response rates than usual (and this has been done in some cases) - allowing greater confidence in this extrapolation to low dose. - In the second, some relation between the parameters of the dose-response curves is obtained at high doses (and this may be done experimentally, in principle, since at high doses the responses are measurable). Then it is decided how the human dose-response curve should be extrapolated to low doses. The advantage here is the possibility of direct comparison between species, albeit at high dose. 15

The difference between these two logically distinct routes of extrapolation might be important in some circumstances. For cancer risk assessment based on animal carcinogenesis bioassays, however, the distinction is glossed over (one might even say, ignored), by the practice of assuming the same (or very similar) mathematical form for the dose-response curve in both humans End animals (or more generally, in all species), and interpreting the parameters in the same way for both compared species. In the general case, however, what is required is some sort of relationship between the parameters of the dose-response curves: Animal Human r = f(d; a,b,c...t) R = F(D; A,B,C...T) We need to be able to derive the parameters A,B,C... from the values a,b,c which can be estimated from experiments, and then use the human dose-response curve to extrapolate to low doses. The prac.tin,al approach is to seek parametrizations of the dose-response curve which result in the derivation of A,B,C... being simple given a,b,c... Consider the case of acute toxicity, for example,. It is found that the shape of the dose-response curve for acute toxicity, in which the response~ is death, is very similar for a large number of toxins and for many different species. There is, in this case, a threshold-type dose-response curve which can be nicely parametrized by two values: the dose at which 50% of the animals tested can be expected to die (under suitable conditions), and the slope of the dose-response curve at this dose. The first parameter is known as the LDS, (the second has no special name). Why is this parametrization useful? If the LDs of various materials in one species are plotted against the LD,,s of the same materials in another species, one finds approximate proportionality between them (the plot is a straight line). This can be expressed as, for example, LD,(rabbit) is proportional to LD50(mouse). Even more remarkable, it turns out (at least, it did for a particular group of chemicals) that if the dose is measured in a suitable way, as (amount)/(surface area of animal), then approximately we have numericai equality in the values of LD.: LD,(rabbit) = LD50(mouse) = LD50(other species) It is this approximate equality which explains the utility of the LD50. The other parameter used in defining the dose-response curve, the slope of the curve at the LD50, is not involved in this 16

relationship. Had we chosen some other method of parametrization, it is quite possible the required interspecies relationship between parameters would be much more complicated. 8 Ini:erspecies Comparison - Constant Relative Potency What is sought is a simple relationship between the parameters of dose-response relationships in different species. When it is assumed that the dose-response relationship includes a term linear in dose, there is a simple measure of the strength of a carcinogen - the carcinogenic potency (the slope of the dose-response curve at low dose). The simplest hypothesis is that for different species, the ratio of carcinogenic potencies is constant for different materials, so that if material A is twice as potent a carcinogen as material B in species 1, it will also be twice as potent as material A in species 2. This is the idea of constant relative potency, as applied to carcinogenesis, and it underlies the standard approaches to estimating human risks from animals. There is even some data which supports this idea! There have been several hundred bioassays performed simultaneously on rats and mice, and when the results of these are parametrized using a close-response relationship which includes a linear term, we can estimate the potency in two species for each material tested. Plotting the potency measured in rats versus the potency measured in mice for each material then gives the figure shown (page 24). Notice that each measurement is uncertain to greater or lesser degree, due to the relatively small numbers of animals tested. If the idea of constant relative potency were exactly correct, these points would all lie on a straight line on the figure - or at least, a!l would lie sufficiently close to such a!ine that the measurement uncertainty bars on each point would encompass the line. From the figures, one can see that: (1) (2) On average, potency in one species is proportional to potency in the other species. There is a large scatter of the points around the lines of exact proportionality - a scatter bigger than would be expected from the measurement errors alone. A similar ~comparison can be attempted between the potencies measured in animal experiments, and those observed in humans (page 24). These cases have arisen in the past where humans have been exposed to materials before they were known to be carcinogenic. We can make use of other's misfortune to estimate how potent each such material is in humans, and compare with estimates obtained for mice and rats in laboratory experiments. In this case, the uncertainties are so large that little can be quantitatively stated, although qualitatively the idea of constant relative potency does not seem to be disproved. A more recent and much more thorough study of comparisons between humans and animals has been carried out for the E.P.A. by Allen, Crump &S'hipp and the qualitative results are similar (page 25) - although Allen et a!. do not quantitativefy evaluate the correlation. 17

9 lnterspecies comparisons - practical and theoretical The measure of carcinogenic potency introduced above was roughly defined as the ratio of (excess tumor probability)/(dose), at low enough dose. For the E.P.A. model usually used in risk assessments: p =1 -exP{-(qo+q,d+q2d2+...+qk-,dk-')! the corresponding measure is q1. When this dose-response relationship is used with real data, it is usual 1!o use an "upper 95% confidence limit" estimate q,* of q, as the measure of potency, since such an estimate is always non-zero (while, for example, the maximum likelihood estimate is often z,ero). The "upper 95% confidence limit" is with respect to the numerical uncertainties of the experiment only, and so this estimate of potency is in no sense an upper limit with respect to all the other uncertainties involved. To compare humans with animals, the approach taken is to postulate a similar dose-response relation ship in both cases: Animal Human p=1 -exp{-(qo+q,d+...)} p = 1 -exp{-(Qo+Q,D+..)} and then ifhe constant relative potency hypothesis suggests that Q, is proportional to q1, and so one hop es to say that: Q, = constant x q,` or at least Q, < constant x q,* where the constant depends only on which animals species is used. We expect the constant to be different for different animal species - it will presumably depend on how we measure dose, on the relative lifespans of animal and human, on relative metabolic rates, and a whole host of other factors. With enough experiments, we could measure the constant in this relationship - at least in comparing animal with animal, rather than human with animal - and (in theory) empirically determine how it varies with these factors. The figures mentioned above suggest that the constant is not completely constant, but that there is some sort of random uncertainty built in (or at least, an uncertainty that we can treat as random), amounting to an average factor of about 5. If we are very lucky, it may be possible to find some way of measuring dose so that the constant in the above relationship is numerically equal to 1, so that the potency is equal in different species (up to the uncertainties) - just as it was possible to find such a measure in the case of the LD,50. 18

It has now become standard practice for risk assessments to assume that the constant is exactly unity if the dose is measured as a (daily average amount)/(surface area of animal), by analogy with the t.D50 case. The graphs shown on page 24 actually suggest that it would be better to assume an average factor of unity, with an uncertainty factor of about 5 to 7, when the dose is measured as a (daily average amount)/(bodyweight of animal). This assumption will probably change some time in the future when better information is available, or when an alternative theoretical framework suggests a better idea. 10 An example - 1,2 Dibromoethane As an example of the procedures usually adopted, let us look at the case of 1,2-Dibromoethane. What fol€ows is by now means complete, but it indicates the sort of analysis which has to be performed. This example is confined to analyzing just one result out of many, in a single bioassay (of about 5). In practice, it is essential to look at all the results. The bioas>ay I have chosen was an inhalation bioassay in the National Toxicology Program series. A summary of the study design for rats (the design for mice is very similar) is: Initial Concentration Time on study (weeks) number of animals ppm (6 hr/d, 5 d/wk) Exposed Observed C Male Rats _ Control 50 0 0 104-106 Low dose 50 10 103 1 High close 50 40 88 0-1 ~_ Female Rats Control 50 0 1 104-106 Low dose 50 10 103 1 High dose 50 40 91 0-1 We will look, only at the results in female rats. First, their survival was not as good as might be desired (see graph below) in such an experiment, but the early mortality was probably largely due to the cancers appearing in the study, so it is acceptable - we can use (at least initially) the 19

simplest analysis based on "end-of-fife" data, without having to worry too much about the age dependence (this should always be backed up by further analysis, of course). TIME ON STUDY (WEEKSI .00 0 15 30 li f0 75 50 126 120 TIME ON STUDY (WEEKS) Figure 2. Survival Curves for Rats Exposed to Air Containin®1, 2-Dibromoethana ; .. _ _•_ a =• , or-- -•+ .......... ....... . -------~---~'tr -------~a oso --~ --- oao 4 0 0 i ~ . o.eo i ' ~ 4 osa i •' Q,~ 1 f FEMALE RATS 0'p ^ UNTAEATEDCDNTRDL 0 LOVIDDSE f ' . 10 0 0 NIGNDDSE . 0 Tumors were found in many tissues. A summary of those tissues where more than 5% of the animals in any group were found with tumors is (for female rats): Control Low High Subcutaneous tissue: fibroma 0/50 0/50 3/50 Subcutaneous tissue: fibroma or fibrosarcoma 0/50 0/50 4/50 Nasal 0avity: Carcinoma, NOS 0/50 0/50 25/50 Nasal 01avity: Squamous cell carcinoma 1/50 1/50 5/50 Nasal C Davity: Adenoma, NOS 0/50 11/50 3/50 Nasal Cavity: Adenocarcinoma, NOS 0/50 20/50 29/50 Nasal E~avity: Adenomatous Polyp, NOS 0/50 5/50 5/50 Nasal Cavity: Papillary Adenoma 0/50 3/50 0/50 Nasal Cavity: Adenoma,NOS; Carcinoma, NOS; Adenocarcinoma,NOS; Papillary Adenoma 1/50 34/50 43/50 Adenomcatous polyp,NOS; and Squamous cell Carcincma Lung: Alveolar/Bronchiolar Carcinoma 0/50 0/48 4/47 Lung: Alveolar/Bronchiolar Carcinoma or Adenoma 0/50 0/48 5/47 Hematopoietic System: All leukemias 6/50 7/50 1/50 20